5440/5439
| Interval information |
thisusoruruyo negative 2nd
reduced
(Shannon, [math]\sqrt{nd}[/math])
5440/5439, the teraosma, is a 37-limit superparticular comma of about 0.32 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 260/259 and 273/272
- 442/441 and 481/480
- 1000/999 and 1225/1224
- 1275/1274 and 1665/1664
- 1296/1295 and 1701/1700
- 1666/1665 and 2401/2400
- 2080/2079 and 3367/3366
- 2500/2499 and 4625/4624
It can be factored into the following superparticular intervals:
- 5776/5775 and 93500/93499
- 5797/5796 and 88320/88319
- 5832/5831 and 80920/80919
- 5888/5887 and 71485/71484
- 5916/5915 and 67600/67599
- 6175/6174 and 45696/45695
- 7106/7105 and 23200/23199
Temperaments
Tempering out this comma in the full 37-limit leads to the rank-11 temperament teraosmic. Using the 2.3.5.7.17.37 subgroup leads to the rank-5 temperament teraoic.
Teraioc
Subgroup: 2.3.5.7.17.37
Comma list: 5440/5439
| [⟨ | 1 | 1 | 2 | 2 | 4 | 7 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | -2 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 1 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.965, ~5/4 = 386.293, ~7/4 = 968.886, ~17/16 = 104.892
Optimal ET sequence: 5, 5gl, 7, 9g, 10, 12l, 15, 17cg, 19g, 22l, 26, 27g, 31l, 41gl, 46, 53, 68, 72, 99, 171, 311, 354, 400, 472, 482, 525, 571, 665, 764, 836, 935, 1236, 1407, 1646, 1718, 1817, 2000, 2072, 2171, 3889, 4824l, 6060l, 6995dl
Badness (Sintel): 0.076
Etymology
This comma was named by Francium in 2025. It refers to 5440 Terao, the asteroid, which in turn was named after Hisashi Terao, the first Japanese professor of astronomy at the University of Tokyo.